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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# T-Insersection Autonomous Driving Scenario\n",
    "This notebook demonstrates a 3-player autonomous driving scenario. Three players are crossing a T-intersection and interact with each others. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "using ALGAMES\n",
    "using BenchmarkTools\n",
    "using LinearAlgebra\n",
    "using StaticArrays\n",
    "using TrajectoryOptimization\n",
    "const TO = TrajectoryOptimization;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the dynamics model of the game."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "struct InertialUnicycleGame{T} <: AbstractGameModel\n",
    "    n::Int  # Number of states\n",
    "    m::Int  # Number of controls\n",
    "    mp::T\n",
    "    pu::Vector{Vector{Int}} # Indices of the each player's controls\n",
    "    px::Vector{Vector{Int}} # Indices of the each player's x and y positions\n",
    "    p::Int  # Number of players\n",
    "end\n",
    "InertialUnicycleGame() = InertialUnicycleGame(\n",
    "    12,\n",
    "    6,\n",
    "    1.0,\n",
    "    [[1,2],[3,4],[5,6]],\n",
    "    [[1,2],[5,6],[9,10]],\n",
    "    3)\n",
    "Base.size(::InertialUnicycleGame) = 12,6,[[1,2],[3,4],[5,6]],3 # n,m,pu,p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Instantiate dynamics model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = InertialUnicycleGame()\n",
    "n,m,pu,p = size(model)\n",
    "T = Float64\n",
    "px = model.px\n",
    "\n",
    "# We use the unicycle dynamics for each player. \n",
    "# State   x = [px1, py1, θ1, v1, px2, py2, θ2, v2, px3, py3, θ3, v3] \n",
    "# Control u = [θ1, v1, θ2, v2, θ3, v3]\n",
    "# px1 = x position of player 1 \n",
    "# py1 = y position of player 1 \n",
    "# θ1 = orientation of player 1 \n",
    "# v1 = x velocity of player 1 \n",
    "\n",
    "function TO.dynamics(model::InertialUnicycleGame, x, u) # Non memory allocating dynamics\n",
    "    qd1 = @SVector [cos(x[3]), sin(x[3])]\n",
    "    qd1 *= x[4]\n",
    "    qd2 = @SVector [cos(x[7]), sin(x[7])]\n",
    "    qd2 *= x[8]\n",
    "    qd3 = @SVector [cos(x[11]), sin(x[11])]\n",
    "    qd3 *= x[12]\n",
    "    qdd1 = u[ @SVector [1,2] ]\n",
    "    qdd2 = u[ @SVector [3,4] ]\n",
    "    qdd3 = u[ @SVector [5,6] ]\n",
    "    return [qd1; qdd1; qd2; qdd2; qd3; qdd3]\n",
    "end;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discretization of the trajectories"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "tf = 3.0  # final time\n",
    "N = 41    # number of knot points\n",
    "dt = tf / (N-1); # time step duration"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Initial and final state definition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define initial and final states (be sure to use Static Vectors!)\n",
    "x0 = @SVector [ # Initial state\n",
    "              -0.50,  -0.15,  0.00,  0.60, #player 1 x,y,θ,v\n",
    "               1.40,   0.15,  pi,    0.60, #player 2 x,y,θ,v\n",
    "               0.43,  -0.30,  pi/2,  0.12, #player 3 x,y,θ,v\n",
    "                ]\n",
    "xf = @SVector [ # Final State\n",
    "               1.30,  -0.15,  0.00, 0.60, #player 1 x,y,θ,v\n",
    "              -0.30,   0.15,  pi,   0.60, #player 2 x,y,θ,v\n",
    "               0.43,   0.35,  pi/2, 0.30, #player 3 x,y,θ,v\n",
    "               ];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define players objective functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define quadratic costs\n",
    "diag_Q1 = @SVector [ # Player 1 state cost\n",
    "    0., 1., 1., 1.,\n",
    "    0., 0., 0., 0.,\n",
    "    0., 0., 0., 0.]\n",
    "diag_Q2 = @SVector [ # Player 2 state cost\n",
    "    0., 0., 0., 0.,\n",
    "    0., 1., 1., 1.,\n",
    "    0., 0., 0., 0.]\n",
    "diag_Q3 = @SVector [ # Player 3 state cost\n",
    "    0., 0., 0., 0.,\n",
    "    0., 0., 0., 0.,\n",
    "    0., 1., 1., 1.]\n",
    "\n",
    "# Players stage state costs\n",
    "Q = [0.1*Diagonal(diag_Q1), \n",
    "     0.1*Diagonal(diag_Q2),\n",
    "     0.1*Diagonal(diag_Q3)]\n",
    "\n",
    "# Players final state costs\n",
    "Qf = [1.0*Diagonal(diag_Q1),\n",
    "      1.0*Diagonal(diag_Q2),\n",
    "      1.0*Diagonal(diag_Q3)]\n",
    "\n",
    "# Players controls costs\n",
    "R = [0.1*Diagonal(@SVector ones(length(pu[1]))),\n",
    "     0.1*Diagonal(@SVector ones(length(pu[2]))),\n",
    "     0.1*Diagonal(@SVector ones(length(pu[3]))),\n",
    "    ]\n",
    "\n",
    "# Players objectives\n",
    "obj = [LQRObjective(Q[i],R[i],Qf[i],xf,N) for i=1:p];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the initial trajectory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "xs = SVector{n}(zeros(n))\n",
    "us = SVector{m}(zeros(m))\n",
    "Z = [KnotPoint(xs,us,dt) for k = 1:N]\n",
    "Z[end] = KnotPoint(xs,m);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Build the T-intersection scenario"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Actors \n",
    "car_radius = 0.08\n",
    "car_radii = [car_radius for i=1:p]\n",
    "actors_types = [:car, :car, :pedestrian] # For visualization\n",
    "\n",
    "#Scene\n",
    "top_road_length = 4.0\n",
    "road_width = 0.60\n",
    "bottom_road_length = 1.0\n",
    "cross_width = 0.25\n",
    "bound_radius = 0.05\n",
    "# Lane indices for each player\n",
    "# Each lane defines a specific drivable area \n",
    "lanes = [1, 2, 5]\n",
    "\n",
    "# Build scenario\n",
    "scenario = TIntersectionScenario(\n",
    "    top_road_length, road_width, bottom_road_length,\n",
    "    cross_width, car_radii, actors_types, bound_radius);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define constraints of the problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create constraint sets\n",
    "conSet = ConstraintSet(n,m,N)\n",
    "con_inds = 2:N # Indices where the constraints will be applied\n",
    "\n",
    "# Add collision avoidance constraints\n",
    "add_collision_avoidance(conSet, car_radii, px, p, con_inds)\n",
    "\n",
    "# Add scenario specific constraints (road boundaries)\n",
    "add_scenario_constraints(conSet, scenario, lanes, px, con_inds; constraint_type=:constraint);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the problem we will be solving"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "prob = GameProblem(model, obj, conSet, x0, xf, Z, N, tf);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Build the ALGAMES solver "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "opts = DirectGamesSolverOptions{T}(\n",
    "    iterations=10,\n",
    "    inner_iterations=20,\n",
    "    iterations_linesearch=10)\n",
    "solver = DirectGamesSolver(prob, opts);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solve the problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  0.036414 seconds (13.62 k allocations: 11.600 MiB)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: (\"Solver iteration = \", 1)\n",
      "└ @ ALGAMES /home/kantorovich/.julia/packages/ALGAMES/gNlVw/src/solvers/direct/direct_methods.jl:39\n",
      "┌ Info: (\"Solver iteration = \", 2)\n",
      "└ @ ALGAMES /home/kantorovich/.julia/packages/ALGAMES/gNlVw/src/solvers/direct/direct_methods.jl:39\n",
      "┌ Info: (\"Solver iteration = \", 3)\n",
      "└ @ ALGAMES /home/kantorovich/.julia/packages/ALGAMES/gNlVw/src/solvers/direct/direct_methods.jl:39\n",
      "┌ Info: (\"Solver iteration = \", 4)\n",
      "└ @ ALGAMES /home/kantorovich/.julia/packages/ALGAMES/gNlVw/src/solvers/direct/direct_methods.jl:39\n",
      "┌ Info: Outer loop converged: cost_tolerance & constraint_tolerance\n",
      "└ @ ALGAMES /home/kantorovich/.julia/packages/ALGAMES/gNlVw/src/solvers/direct/direct_methods.jl:146\n"
     ]
    }
   ],
   "source": [
    "@time solve!(solver);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluate the solve time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  33.530 ms (15403 allocations: 11.39 MiB)\n"
     ]
    }
   ],
   "source": [
    "opts = DirectGamesSolverOptions{T}(\n",
    "    iterations=10,\n",
    "    inner_iterations=20,\n",
    "    iterations_linesearch=10,\n",
    "    log_level=ALGAMES.Logging.Warn)\n",
    "solver = DirectGamesSolver(prob, opts)\n",
    "@btime timing_solve(solver);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualize state and control trajectories"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = TO.states(solver)\n",
    "U = TO.controls(solver)\n",
    "visualize_state(X)\n",
    "visualize_control(U,pu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</svg>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "visualize_optimality_merit(solver)\n",
    "visualize_α(solver)\n",
    "visualize_cmax(solver)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create a 3D visualization in MeshCat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MeshCat.Animation(Dict{MeshCat.SceneTrees.Path,MeshCat.AnimationClip}(), 30)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vis=ALGAMES.Visualizer()\n",
    "anim=ALGAMES.MeshCat.Animation()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "    <div style=\"height: 500px; width: 100%; overflow-x: auto; overflow-y: hidden; resize: both\">\n",
       "    <iframe src=\"http://localhost:8703\" style=\"width: 100%; height: 100%; border: none\"></iframe>\n",
       "    </div>\n"
      ],
      "text/plain": [
       "MeshCat.DisplayedVisualizer(MeshCat.CoreVisualizer(MeshCat.SceneTrees.SceneNode(nothing, nothing, Dict{String,Array{UInt8,1}}(), Dict{String,MeshCat.SceneTrees.SceneNode}()), Set(Any[]), ip\"127.0.0.1\", 8703))"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ALGAMES.MeshCat.render(vis) # To open the visualizer in the notebook\n",
    "# ALGAMES.MeshCat.open(vis) # To open the visualizer in a new tab"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Animate the scene"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "vis, anim = animation(solver, scenario;\n",
    "    vis=vis, anim=anim,\n",
    "    open_vis=false);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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